Effects of density-dependent migrations on stability of a two-patch predator–prey model

Abdllaoui, Abderrahim El; Auger, Pierre; Kooi, Bob W.; Parra, Rafael; Mchich, Rachid

doi:10.1016/j.mbs.2007.03.002

Cited by 47 publications

(41 citation statements)

References 26 publications

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“…Still, non-diffusive movement (caused, e.g. by prey-handling time effects) can by itself generate oscillation [1,27]. The rapid evolution of migration probabilities can also produce non-equilibrium dynamics [62].…”

Section: Introductionmentioning

confidence: 99%

Effect of resource subsidies on predator–prey population dynamics: a mathematical model

Nevai

Gorder

2012

Journal of Biological Dynamics

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The influence of a resource subsidy on predator-prey interactions is examined using a mathematical model. The model arises from the study of a biological system involving arctic foxes (predator), lemmings (prey), and seal carcasses (subsidy). In one version of the model, the predator, prey and subsidy all occur in the same location; in a second version, the predator moves between two patches, one containing only the prey and the other containing only the subsidy. Criteria for feasibility and stability of the different equilibrium states are studied both analytically and numerically. At small subsidy input rates, there is a minimum prey carrying capacity needed to support both predator and prey. At intermediate subsidy input rates, the predator and prey can always coexist. At high subsidy input rates, the prey cannot persist even at high carrying capacities. As predator movement increases, the dynamic stability of the predator-prey-subsidy interactions also increases.

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Section: Introductionmentioning

confidence: 99%

Effect of resource subsidies on predator–prey population dynamics: a mathematical model

Nevai

Gorder

2012

Journal of Biological Dynamics

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“…prey leave faster a given patch when more predators are there at that time [12--14]. Abdllaoui et al [15] studied the coupling of these two kinds of density-dependent migrations in a predator-prey model. However, to the best of our knowledge, migration of middle predator in tri-trophic food chain model has not yet been explored.…”

Section: Introductionmentioning

confidence: 99%

Migratory effect of middle predator in a tri-trophic food chain model

Chowdhury¹,

Chakraborty

Chattopadhyay

2010

Math. Meth. Appl. Sci.

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A tri-trophic food chain model in a two-patch environment is considered. Although tri-trophic food chain model is well studied, the study considering migration of middle predator is lacking. To the best of our knowledge, the present investigation is the first study in this direction. Both prey and predator density-dependent migrations are considered to observe the effects on stability and persistence of the system. We observe that migration of middle predator has the ability to control chaos in tri-trophic food chain model. Our results indicate that the chance of predator extinction enhances for prey density-dependent middle predator migration.

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“…In fact, at some levels, immigration can destabilize top predator populations. Abdllaoui et al (2007) similarly found that limit cycles can emerge as density-dependent migration increases in two-patch predator and prey models. When considering larger numbers of patches in a lattice, Blasius et al (1999) found that not only did populations cycle, but the populations became phase synchronized, although local peak populations were uncorrelated.…”

Section: Migration-driven Limit Cyclesmentioning

confidence: 86%

Immigration can destabilize tri-trophic interactions: implications for conservation of top predators

et al. 2015

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Top predators often have large home ranges and thus are especially vulnerable to habitat loss and fragmentation. Increasing connectance among habitat patches is therefore a common conservation strategy, based in part on models showing that increased migration between subpopulations can reduce vulnerability arising from population isolation. Although three-dimensional models are appropriate for exploring consequences to top predators, the effects of immigration on tri-trophic interactions have rarely been considered. To explore the effects of immigration on the equilibrium abundances of top predators, we studied the effects of immigration in the three-dimensional Rosenzweig-MacArthur model. To investigate the stability of the top predator equilibrium, we used MATCONT to perform a bifurcation analysis. For some combinations of model parameters with low rates of top predator immigration, population trajectories spiral towards a stable focus. Holding other parameters constant, as immigration rate is increased, a supercritical Hopf bifurcation results in a stable limit cycle and thus top predator populations that cycle between high and low abundances. Furthermore, bistability arises as immigration of the intermediate predator is increased. In this case, top predators may exist at relatively low abundances while prey become extinct, or for other initial conditions, the relatively higher top predator abundance controls intermediate predators allowing for non-zero prey population abundance and increased diversity. Thus, our results reveal one of two outcomes when immigration is added to the model. First, over some range of top predator immigration rates, population abundance cycles between high and low values, making extinction from the trough of such cycles more likely than otherwise. Second, for relatively higher intermediate predator migration rates, top predators may exist at low values in a truncated system with impoverished diversity, again with extinction more likely.

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Effects of density-dependent migrations on stability of a two-patch predator–prey model

Cited by 47 publications

References 26 publications

Effect of resource subsidies on predator–prey population dynamics: a mathematical model

Effect of resource subsidies on predator–prey population dynamics: a mathematical model

Migratory effect of middle predator in a tri-trophic food chain model

Immigration can destabilize tri-trophic interactions: implications for conservation of top predators

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